A methodological approach of estimating resistance to flow under unsteady flow conditions

Abstract

Abstract. This paper presents an evaluation and analysis of resistance parameters: friction slope, friction velocity and Manning coefficient in unsteady flow. The methodology to enhance the evaluation of resistance by relations derived from flow equations is proposed. The main points of the methodology are (1) to choose a resistance relation with regard to a shape of a channel and (2) type of wave, (3) to choose an appropriate method to evaluate slope of water depth, and (4) to assess the uncertainty of result. In addition to a critical analysis of existing methods, new approaches are presented: formulae for resistance parameters for a trapezoidal channel, and a translation method instead of Jones' formula to evaluate the gradient of flow depth. Measurements obtained from artificial dam-break flood waves in a small lowland watercourse have made it possible to apply the method and to analyse to what extent resistance parameters vary in unsteady flow. The study demonstrates that results of friction slope and friction velocity are more sensitive to applying simplified formulae than the Manning coefficient (n). n is adequate as a flood routing parameter but may be misleading when information on trend of resistance with flow rate is crucial. Then friction slope or friction velocity seems to be better choice.

A Hydraulic Friction Model for One-Dimensional Unsteady Channel Flows with Experimental Demonstration

“…The most significant difference between unsteady and steady uniform flows is that the flow conditions in an unsteady flow have nonuniformity and unsteadiness. The partial derivatives of hydraulic parameters are the most relevant physical variables to describe flow unsteadiness and flow nonuniformity in 1D problems [5]. The dependence of unsteady flow resistance on derivatives (e.g., ∂u/∂t, ∂u/∂x, and ∂h/∂x) is significant [1,2].…”

“…A significant difference was observed between steady uniform and unsteady frictions. For example, Mrokowska et al reported that the steady-state formula for frictional slope and shear velocity is not applicable to unsteady flow [5]. Fread reported that the trend of Manning coefficient vs. flow rate decreases when the inundation area is relatively small compared to an in-bank flow area, or increases in the reversed case, indicating that the Manning coefficient is a misleading parameter to investigate the relationship between resistance and flow rate [6].…”

“…For example, Sutter et al reported that the capacity of sediment transport increases when the unsteadiness of flow increases; this can be considered as the result of the effect of flow unsteadiness on shear stress [10]. Further, in unsteady flows, a hysteresis effect was detected; a phase lag was observed between flow depth and mean cross-sectional velocity peaks [3,5]. The hysteresis effect results in different characteristics of flow resistance in the rising and falling limbs of a hydrograph [11].…”

Non-uniform flow over cobble bed with submerged vegetation strip

“…Equation 1 contains the flow depth gradient, which is extremely difficult to determine. Mrokowska et al (2015aMrokowska et al ( , 2015b recently discussed this issue and claimed it was highly sensitive to the method used for computations. In this study, to calculate β, the variation in water depth along the flow direction (∂H/∂x) was determined from the continuous water surface profile, adjusted by a spline fitting technique to the flow depth measurements.…”

Laboratory studies on bedload transport under unsteady flow conditions

“…A definition of bed shear stress under mobile bed conditions is not straightforward (Ferreira et al, 2012;Nikora et al, 2007), and for this reason the measurements of bed shear stress require cautious interpretation. Moreover, it should be noted that methods that may be applied under unsteady flow are scarce, mainly due to theoretical assumptions (Mrokowska et al, 2015a). Formulae derived from Saint-Venant model have become popular in unsteady flow experiments (Bombar, 2016;Song and Graf, 1996;Mrokowska et al, 2015b).…”